哈佛大学医学统计学课程1.pdf

Dr. Elkan Halpern DOES NOT HAVE ANY FINANCIAL RELATIONSHIPS WITH A COMMERCIAL ENTITY PRODUCING HEALTH-CARE RELATED PRODUCTS AND/OR SERVICES Power April 9, 2014 You suspect that a new treatment improves the chances of survival over the known chance of 1/7 associated with standard therapy. You suspect that a new treatment increases the chances of a specific a.e. over the known chance of 1/7 associated with standard therapy. You can obtain the clinical records of 21 consecutive patients who were treated with this new treatment at MGH. You can determine the outcome (survival Y/N or a.e. Y/N) for each. Is it worth the effort? HYPOTHESIS TESTING You want to test the null hypothesis H : p = 1/7 0 against the alternative H : p 1/7 1 Distribution of # cases among 21 patients if the chance of the outcome is 1/7 Patients # Cases 21 0 0.0393 1 0.1375 2 0.2291 3 0.2418 4 0.1814 5 0.1028 6 0.0457 7 0.0163 8 0.0048 9 0.0011 10 0.0002 11 0.0000 Cumulative probabilities of dist. of #cases, y, among 21 patients if chance is 1/7 #y P (Y=y) P (Yy) P (Yy) 0 0.0393 0.0393 1.0000 1 0.1375 0.1767 0.9607 2 0.2291 0.4058 0.8233